In this number analogy, 342 is related to 453 in a particular way. Using the same pattern, which number should replace the question mark in 342 : 453 :: 831 : ?

Introduction / Context:
This question belongs to the category of number analogies, where a transformation applied to one number must be identified and then applied to another number. These questions check numerical pattern recognition and the ability to perform simple operations like addition, subtraction, or multiplication consistently.

Given Data / Assumptions:
We are given the pair 342 : 453. We must relate 831 to an unknown number using the same transformation. Only basic arithmetic operations are expected. Exactly one option should satisfy the same relationship.

Concept / Approach:
The safest approach is to compare 342 and 453 numerically. First, check for direct arithmetic relations such as adding or subtracting a constant. If that fails, we can explore digit wise patterns. In this problem, a direct comparison of the whole numbers reveals a simple constant difference, which is the most natural interpretation for a reasoning exam.

Step-by-Step Solution:
Step 1: Compute the difference between 453 and 342. 453 - 342 = 111. Step 2: Interpret the relationship. The second number is obtained by adding 111 to the first number. So, 342 + 111 = 453. Step 3: Apply the same transformation to 831. 831 + 111 = 942. Step 4: Match the result with the options. 942 is present as an option, so it is the candidate answer.

Verification / Alternative check:
As a quick verification, we can check whether any other option maintains some similar consistent pattern, such as subtracting 111. For example, 831 - 111 = 720, which is also among the options but would correspond to a subtraction pattern. However, 342 to 453 clearly uses addition, not subtraction. Therefore only 942 satisfies the same direction and magnitude of change. This removes any ambiguity and confirms that the rule is add 111 to the first term.

Why Other Options Are Wrong:
720 is obtained by 831 - 111, which reverses the operation and does not match the example pair. 740 has a difference of 91 from 831, which does not equal 111 and so breaks the pattern. 922 differs from 831 by 91, which again does not match the consistent difference of 111 observed in the first pair. 933 differs from 831 by 102, so it clearly does not follow the transformation seen with 342 and 453.

Common Pitfalls:
A common mistake in number analogy problems is to overcomplicate the pattern by focusing on digits individually when a simple whole number operation is sufficient. Candidates also sometimes confuse addition and subtraction if both seem to produce some option. The key is always to stick to the direction of the transformation shown in the example pair. Here the first number increases, so the same increase must apply in the second pair as well. Double checking the numeric difference avoids careless errors and stabilises performance in such questions.

Final Answer:
The number that correctly completes the analogy is 942.